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Search Results (565)

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18 pages, 34985 KB  
Article
In Situ Fabrication of BiOCl@Bi2S3@ZnIn2S4 Double Z-Scheme Heterojunctions for Enhanced Photocatalytic Degradation Performance
by Ligang Ma, Tingting Chen, Jingxuan Zhou, Jiulei Zhao, Xinlan Li, Huilin Jiang, Liping Li and Xiaoqian Ai
Molecules 2026, 31(16), 2843; https://doi.org/10.3390/molecules31162843 - 14 Aug 2026
Abstract
Organic pollutants in industrial wastewater present a severe threat to both the environment and human health. Photocatalytic technology, recognized for its eco-friendliness and high efficiency, has become a leading approach for degrading such pollutants. In this work, BiOCl nanosheets were first synthesized using [...] Read more.
Organic pollutants in industrial wastewater present a severe threat to both the environment and human health. Photocatalytic technology, recognized for its eco-friendliness and high efficiency, has become a leading approach for degrading such pollutants. In this work, BiOCl nanosheets were first synthesized using a hydrothermal method. Subsequently, an anion exchange reaction with TAA in an oil bath generated a Bi2S3 intermediate layer on the BiOCl surface, followed by the in situ growth of ZIS nanostructures, successfully constructing a BiOCl@Bi2S3@ZIS double Z-scheme heterojunction. By adjusting the amount of BiOCl, the interface contact and dispersion of the heterojunction were optimized. Characterization results demonstrate that the BiOCl@ZIS-25 heterojunction possesses the highest specific surface area (103.5 m2·g−1) and the most efficient charge separation. Under visible light irradiation, it achieved 97.88% degradation of methylene blue within 20 min, with a reaction rate constant 8 and 4 times higher than those of pure BiOCl and ZIS, respectively. Mechanistic investigations indicate that Bi2S3 interlayer acts as an electron-transfer bridge between BiOCl and ZIS, establishing a double Z-scheme charge transfer pathway that significantly enhanced the separation and utilization efficiency of photogenerated charge carriers. This study offers valuable insights for designing highly efficient and stable photocatalytic composite materials. Full article
(This article belongs to the Section Photochemistry)
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15 pages, 1148 KB  
Article
Ro-Vibrational and Pure Vibrational Partition Functions and Thermodynamic Properties in an Eckart-like Potential Model
by Clement Atachegbe Onate, Matthew Olanrewaju Oluwayemi and Olumide Oyewale Ajani
AppliedMath 2026, 6(8), 130; https://doi.org/10.3390/appliedmath6080130 - 11 Aug 2026
Viewed by 64
Abstract
This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression [...] Read more.
This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression of the energy eigenvalues is obtained. The ro-vibrational Z is computed by explicitly incorporating the rotational quantum number, a feature often neglected or misapplied in many studies. This result is used to evaluate the key thermodynamic properties (TP), including the Gibbs free energy (G), entropy (S), and enthalpy (H). Numerical analysis reveals that the Z increases monotonically with temperature, while the G decreases in accordance with statistical thermodynamics. The S exhibits saturation-like behaviour at higher temperatures, while the H displays convex growth with increasing thermal energy. Parametric studies demonstrate that the Eckart-like potential allows for the controlled tuning of TP, with variations in the potential parameters, including the screening parameter, having distinct effects. The results generalise existing models, reproduce the Hulthén potential under specific conditions, show the effect of the rotational quantum number of TP, and provide new insights into the ro-vibrational statistical mechanics of exponential-type potentials. Full article
(This article belongs to the Section Deterministic Mathematics)
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18 pages, 10481 KB  
Article
Enhanced Approach Procedures Based on OAS Constraints and BDSBAS Performance Evaluation
by Jinyu Wang, Shuaiyong Zheng, Yibo Zhou, Bo Shao and Xiao Liang
Aerospace 2026, 13(8), 717; https://doi.org/10.3390/aerospace13080717 - 10 Aug 2026
Viewed by 174
Abstract
Traditional Instrument Landing Systems (ILSs) suffer from inherent limitations, including limited signal coverage and high maintenance costs. To address these issues, we propose a novel approach procedure design method based on the BeiDou Satellite-Based Augmentation System (BDSBAS), which is particularly suitable for airports [...] Read more.
Traditional Instrument Landing Systems (ILSs) suffer from inherent limitations, including limited signal coverage and high maintenance costs. To address these issues, we propose a novel approach procedure design method based on the BeiDou Satellite-Based Augmentation System (BDSBAS), which is particularly suitable for airports with complex terrain conditions or no ground-based navigation infrastructure. In this method, a geometric constraint model of the approach trajectory is constructed in a local Cartesian coordinate system, and obstacle clearance performance is evaluated based on the Obstacle Assessment Surface (OAS) theory. Global Navigation Satellite System (GNSS) observations and BDSBAS augmentation data are processed collaboratively to calculate aircraft position solutions, as well as the corresponding horizontal and vertical protection levels, enabling comprehensive evaluation of the navigation system’s accuracy, integrity, continuity, and availability. The feasibility and performance of the proposed method are verified through practical airport deployment and dynamic flight tests. Experimental results show that the 95th-percentile horizontal and vertical position errors reach 1.31 m and 4.17 m, respectively, and all valid observation epochs fully comply with the protection level and alert limit specifications. Compared with the conventional ILS-based scheme, the proposed method reduces the total OAS area and the missed-approach Z-surface area by 44.25% and 67.90%, respectively. The findings demonstrate that BDSBAS can effectively support approach procedure design and guarantee high-precision navigation performance, while significantly reducing the reliance on airport-specific ground navigation infrastructure. Full article
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31 pages, 2984 KB  
Article
Spatial All-Azimuth Versus Single-Sided Planar Identifiers for Warehouse Robot Navigation: A Factorial Simulation Study
by Kamil Kušnirák, Oto Haffner, Erik Kučera and Ondrej Kolimár
Eng 2026, 7(8), 394; https://doi.org/10.3390/eng7080394 - 7 Aug 2026
Viewed by 122
Abstract
A camera-guided warehouse robot keeps its bearings by repeatedly estimating its pose against known visual references, and it must relocalize whenever that estimate is lost. What limits this process is often not identification but the availability of a usable reference along the route. [...] Read more.
A camera-guided warehouse robot keeps its bearings by repeatedly estimating its pose against known visual references, and it must relocalize whenever that estimate is lost. What limits this process is often not identification but the availability of a usable reference along the route. The references used in practice are usually single-sided planar fiducial markers such as QR-like codes, ArUco markers, and AprilTags, which stay readable only within a limited cone about their surface normal; a spatial reference, by contrast, can in principle be recognized from any azimuth. We quantify what that difference is worth at the navigation level. The framework is built in Unity with NavMesh navigation and a purely geometric-availability model, rather than an image-based recognizer, whose single switchable property is the availability rule. In the idealized all-azimuth spatial-reference regime (the spatial regime), a reference is available from any direction; in the single-sided, angularly constrained planar-reference regime (the planar regime) it is available only within ±20° of the surface normal. A full-factorial experiment with 54 configurations (3×3×2×3) and n=100 paired replications, 10,800 runs in all, was run in both regimes over four deployment factors: deployment scheme, camera field of view, recovery step, and detection range. Under this geometric model, the spatial regime reached 5.7× higher reference coverage (41.6% vs. 7.3%) and a mission-completion rate 30 percentage points higher (86.2% vs. 55.9%). A paired Wilcoxon signed-rank test confirms the coverage difference (p<0.001, matched-pairs dz=1.84), and McNemar’s test together with a logistic regression confirms the completion difference. In a factorial analysis of variance, the detection range dominates (partial η2=0.903), and a strong deployment × range interaction concentrates the advantage in the rack aisles, where a planar reference is seen edge-on. Three further analyses point the same way: an angular-threshold sweep from 10° to 60°, an equal-count deployment control, and route- and time-normalized visibility and relocalization metrics. The advantage also held across square, L-shaped, and U-shaped aisle layouts (32,400 runs in total), with a negligible regime × layout interaction. All these numbers are model-based estimates under an explicitly stated availability model: they measure the navigation-level value of azimuthal reference availability and do not validate any particular physical object, decoding algorithm, or AR device. Full article
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22 pages, 69237 KB  
Article
Experimental and Numerical Investigation of Cold-Formed Steel Storage Platforms with Perforated Channel Beams
by Szymon Swierczyna
Materials 2026, 19(15), 3316; https://doi.org/10.3390/ma19153316 - 4 Aug 2026
Viewed by 245
Abstract
This paper presents the results of experimental investigations of the flexural capacity of the main beams in a storage platform with plan dimensions of 5.0 m × 2.0 m. The platform was designed as a grid structure, with main beams made of cold-formed [...] Read more.
This paper presents the results of experimental investigations of the flexural capacity of the main beams in a storage platform with plan dimensions of 5.0 m × 2.0 m. The platform was designed as a grid structure, with main beams made of cold-formed channel sections and crossbeams made of sigma-section members. The crossbeams, spaced at 0.6 m, were connected to the main beams using M12 bolts and angle cleats. Eight test specimens were examined, with section heights ranging from 250 to 500 mm and wall thicknesses of 3 or 4 mm, fabricated from S350GD+Z steel. Loading was applied in a four-point bending scheme until failure of one of the main beams, while recording the moment–deflection relationship. The obtained failure loads were compared with the design resistances calculated in accordance with EN 1993-1-3. Additionally, GMNIA analyses were performed for the tested storage-platform structures using the Idea StatiCa Member version 24.1 software, incorporating measured material properties and equivalent geometric imperfections in accordance with prEN 1993-1-14. The adopted procedure included a sensitivity study to investigate the influence of different combinations of local and distortional buckling mode imperfections on the numerical results. The observed behaviour was characterized by interaction between distortional and local buckling modes, accompanied by yielding in the compression zone. The GMNIA analyses predicted the ultimate bending resistance with good accuracy, yielding FEM-to-test resistance ratios between 0.93 and 0.98. The sensitivity study indicated that the predicted ultimate resistance was only weakly affected by the assumed combination of local and distortional imperfection modes. For the investigated platform systems, the effective section approach according to Eurocode 3 provided accurate predictions of the ultimate resistance, with calculated-to-test resistance ratios ranging from 0.96 to 1.01. This agreement is discussed in the context of the possible stiffening effect of crossbeam-to-web connections. Full article
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19 pages, 27575 KB  
Article
A p–n Junction-Assisted Z-Scheme Cu2O–SnO2/g-C3N4 Heterojunction for Highly Efficient Visible-Light Photocatalysis
by Zibin Hai, Jingwei Han, Mengyao Xue and Yunhua Zhang
Catalysts 2026, 16(8), 707; https://doi.org/10.3390/catal16080707 - 4 Aug 2026
Viewed by 240
Abstract
In semiconductor photocatalysis, the strong redox ability of a wide band gap and the broad light absorption range of a narrow band gap are a pair of irreconcilable trade-offs. By combining semiconductors with different band gap widths and band edge positions, both of [...] Read more.
In semiconductor photocatalysis, the strong redox ability of a wide band gap and the broad light absorption range of a narrow band gap are a pair of irreconcilable trade-offs. By combining semiconductors with different band gap widths and band edge positions, both of these advantages can be achieved simultaneously. A ternary Cu2O-SnO2/g-C3N4 (CuSnCN) composite photocatalyst was prepared through the hydrothermal and calcination method. Structural analyses confirm the successful integration of truncated octahedral Cu2O, spherical SnO2, and layered g-C3N4, which extends the visible-light response to 650 nm. The optimized system achieves a remarkable 96.58% degradation of methyl orange (80 min, 0.2 g/L catalyst, pH = 3) through dual heterojunction synergies: p–n junctions (Cu2O/g-C3N4 and SnO2/g-C3N4) and Z-scheme charge transfer (SnO2/Cu2O), with •O2/h+ identified as the dominant reactive species. This work establishes a tunable heterojunction platform for the elimination of multiple pollutants through engineered radical-generation pathways. Full article
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33 pages, 4403 KB  
Article
A Dual-Cuboid Constraint Method with Marching Cubes-Based Contour Extraction for Verticality Inspection of Square Tower Structures
by Mingduan Zhou, Zihan Zhou, Yuhan Qin, Guanxiu Wu, Qiao Song, Shiqi Lin, Lu Qin, Peng Yan and Shufa Li
Sensors 2026, 26(15), 4918; https://doi.org/10.3390/s26154918 - 4 Aug 2026
Viewed by 334
Abstract
Verticality inspection of square tower structures is of great significance for ensuring structural operational safety, extending service life, and optimizing maintenance strategies. However, conventional verticality inspection methods still exhibit deficiencies in point cloud noise suppression, removal of internal redundant points, and stable geometric [...] Read more.
Verticality inspection of square tower structures is of great significance for ensuring structural operational safety, extending service life, and optimizing maintenance strategies. However, conventional verticality inspection methods still exhibit deficiencies in point cloud noise suppression, removal of internal redundant points, and stable geometric feature extraction, which often lead to fluctuations in axis fitting results and fail to meet the requirements of non-contact, high-precision, and holistic perception-based verticality inspection for square tower structures. To address the above issues, this paper proposes a Dual-Cuboid Constraint Method with Marching Cubes-Based Contour Extraction for Verticality Inspection of Square Tower Structures. First, raw point cloud data of the surface of square tower structures were acquired through terrestrial LiDAR multi-station scanning. After preprocessing, including point cloud registration, coordinate system unification, redundancy removal, and denoising, high-precision effective point cloud data were obtained in a unified station-centered spatial coordinate system. Subsequently, the initial body center point coordinates and principal axis directions of the standard segment point clouds were determined using the principal axis projection method. Based on these results, a dual-cuboid constraint frame was constructed, and the shell point clouds of the standard segments were extracted through outer-frame enclosure and inner-frame exclusion. The principal axis projection method was then applied again to calculate the body center point coordinates of the shell point cloud for each standard segment. The central axis of the body center point set was subsequently fitted using the least squares method to determine the unit direction vector of the structural central axis. Finally, within the station-centered spatial coordinate system, vector operations were performed between the unit direction vector and the x-axis and z-axis, respectively, to calculate the tilt attitude parameters of the square tower structure, including the azimuth angle of inclination, the inclination angle, and the verticality. The detection results obtained from different schemes were then comparatively evaluated using the relative error metric. Field validation was conducted on a tower crane at a construction site in Beijing. Four dual-cuboid constraint frame schemes with dimensional errors of 20 mm, 40 mm, 60 mm, and 80 mm were designed. Furthermore, based on the experimental process of the method presented in this paper, an unconstrained solution was established as a comparison experiment, and it was compared with the two reference experiments based on the Marching Square algorithm and the RANSAC algorithm. The results indicated that the tower-body verticality values obtained using the four dual-cuboid constraint frame schemes with different dimensional errors were 3.48‰, 3.63‰, 3.60‰, and 3.82‰, respectively, with a mean value of 3.63‰ and a range of only 0.34‰. The verticality results obtained from the four constrained schemes were generally consistent and showed good agreement with those obtained from 3.03‰ and 3.14‰, and reasonable proximity to the result obtained from 2.82‰, respectively. The results further suggest that the proposed dual-cuboid constraint frame contributes to improving the stability of point cloud feature extraction and central axis fitting, and yields generally consistent detection results across different dimensional error parameters, indicating that the method exhibits robustness to variations in the constraint-frame dimensions within the tested parameter ranges. Full article
(This article belongs to the Section Radar Sensors)
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29 pages, 10336 KB  
Article
Synthesis and Property Detection of the Ho2BiNbO7/ZnBiTmO4 Composite Catalyst for Photocatalytic Degradation of Brilliant Green
by Jingfei Luan and Boyang Liu
Nanomaterials 2026, 16(15), 951; https://doi.org/10.3390/nano16150951 - 2 Aug 2026
Viewed by 257
Abstract
A high-performance Z-scheme Ho2BiNbO7/ZnBiTmO4 heterojunction (HZ) photocatalyst was prepared for the first time using a wet impregnation method. The HZ photocatalyst significantly improved the separation efficiency of the photoinduced electrons and the photoinduced holes; meanwhile, the HZ photocatalyst [...] Read more.
A high-performance Z-scheme Ho2BiNbO7/ZnBiTmO4 heterojunction (HZ) photocatalyst was prepared for the first time using a wet impregnation method. The HZ photocatalyst significantly improved the separation efficiency of the photoinduced electrons and the photoinduced holes; meanwhile, the HZ photocatalyst could effectively broaden the visible light spectrum via a specific mechanism of the Z-scheme heterojunction structure. The experimental results displayed that the HZ photocatalyst had strong catalytic activity when the brilliant green (BLG) was degraded. In particular, the degradation rate of BLG when using the HZ photocatalyst was found to be 99.47%, and the mineralization efficiency of the total organic carbon (TOC) concentration was found to be 98.26% when using the HZ photocatalyst under visible light irradiation (VILIIR). The HZ photocatalyst possessed higher photocatalytic activity compared with Ho2BiNbO7, ZnBiTmO4, or N-doped TiO2 (N-T). The degradation rate of BLG when using the HZ photocatalyst was 1.27 times higher than that when using Ho2BiNbO7, 1.15 times higher than that when employing ZnBiTmO4, or 2.91 times higher than that when using N-T under VILIIR. The mineralization efficiency of the TOC concentration after catalytic degradation of BLG when employing the HZ photocatalyst was 1.31 times higher than that when employing Ho2BiNbO7, 1.19 times higher than that when employing ZnBiTmO4, or 3.14 times higher than that when using N-T under VILIIR. The experimental generating radicals confirmed that the HZ photocatalyst might produce diverse reactive radicals, which contained superoxide anions (•O2), hydroxyl radicals (•OH) and photogenerated holes (h+) after catalytic degradation of BLG. The descending order of oxidizing capacity for above three radicals was as follows: •OH > •O2 > h+. The descending order of the photocatalytic activity for the four photocatalysts was as follows: HZ > ZnBiTmO4 > Ho2BiNbO7 > N-T. The intermediate degradation products of BLG were detected by employing the HZ photocatalyst during the photocatalytic degradation process of BLG; the reliability, reusability, and stability of the HZ photocatalyst were proven by quintic cyclical degradation experiments of BLG. This study developed the degradation pathways and degradation mechanism of BLG when using the HZ photocatalyst under VILIIR. This work supplies novel thought for the design and manufacture of Z-scheme heterojunction catalysts, and it provides a basis for developing an efficient environmental remediation technique for BLG pollution. Full article
(This article belongs to the Special Issue Heterogeneous Photocatalysts Based on Nanocomposites (Second Edition))
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23 pages, 3487 KB  
Article
Grouping-Based and Position-Based Phase Optimization for RIS-Assisted Millimeter-Wave Vehicular Communications
by Zongliang Xu, Guicai Yu and Yingcong Luo
Sensors 2026, 26(15), 4862; https://doi.org/10.3390/s26154862 - 2 Aug 2026
Viewed by 150
Abstract
Millimeter-wave vehicular communication links are prone to blockage and suffer from severe path loss, and high mobility leads to rapidly time-varying channels. In addition, large-scale reconfigurable intelligent surface (RIS) arrays impose substantial channel-estimation overhead and phase-optimization complexity. To address these issues, a group-based [...] Read more.
Millimeter-wave vehicular communication links are prone to blockage and suffer from severe path loss, and high mobility leads to rapidly time-varying channels. In addition, large-scale reconfigurable intelligent surface (RIS) arrays impose substantial channel-estimation overhead and phase-optimization complexity. To address these issues, a group-based and position-aided phase-optimization method is proposed for RIS-assisted millimeter-wave vehicular communications. First, an RIS-assisted uplink system is modeled with a multi-antenna base station (BS), an RIS configured as a uniform planar array (UPA) and a single-antenna vehicular terminal. Channel expressions are formulated for the direct vehicle–BS link, the vehicle–RIS link and the RIS–BS link. Rician fading, line-of-sight (LoS)-dominated millimeter-wave propagation, mobility-induced Doppler shifts and a standardized path-loss model for urban microcell street-canyon scenarios are incorporated to characterize the RIS-assisted vehicular cascaded channel. Based on this model, an optimization problem for the RIS phase-shift matrix is formulated under discrete phase-shift constraints to maximize the achievable rate per unit bandwidth. To avoid the exponential increase in complexity caused by conventional exhaustive search as the number of RIS reflecting elements increases, a successive refinement algorithm is introduced to derive an equivalent channel-gain expression. The original phase-optimization problem is then transformed into an element-wise iterative update process, thereby reducing the computational complexity of large-scale RIS phase configuration. To further reduce the reliance on full channel state information (CSI), two low-overhead phase-optimization schemes are designed. In the group-based scheme, the RIS reflecting elements are partitioned into several subgroups, with all elements in each subgroup constrained to share the same phase shift. This design reduces both the channel-estimation dimensionality and the number of optimization variables. In the position-aided scheme, the spatial coordinates of the BS, RIS and vehicle are used to derive the link distances and the associated angles of arrival and departure. Based on these geometric parameters, the vehicle–RIS–BS cascaded channel is reconstructed and a corresponding phase-alignment strategy is designed. The simulation results demonstrate that both proposed schemes achieve rates of approximately 6.5 bits s1Hz1 at a transmit power of 30 dBm and outperform existing phase-optimization techniques. When the successive refinement algorithm is applied, the computation time required for phase optimization with a 256-element RIS remains below 0.01 s. Under high-mobility conditions, both proposed schemes approach the performance upper bound achieved with perfect CSI, demonstrating strong robustness to channel variations. Full article
(This article belongs to the Section Electronic Sensors)
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72 pages, 2523 KB  
Article
Decentralized Self-Verifiable Cryptographic Image Provenance in Social Internet of Things
by Junaid Akram, Awais Akram and Ali Anaissi
Future Internet 2026, 18(8), 402; https://doi.org/10.3390/fi18080402 - 30 Jul 2026
Viewed by 274
Abstract
Smart objects in the Social Internet of Things (SIoT), such as cameras, drones, and vehicles, exchange images that act as visual evidence and drive automated decisions. These images can be altered in their pixels or their metadata, replayed, or injected by unauthorized publishers. [...] Read more.
Smart objects in the Social Internet of Things (SIoT), such as cameras, drones, and vehicles, exchange images that act as visual evidence and drive automated decisions. These images can be altered in their pixels or their metadata, replayed, or injected by unauthorized publishers. Central verification services can check them, but such services must be reachable at verification time, form a bottleneck, and observe who produced which image. This paper presents a decentralized scheme that makes an SIoT image object self-verifiable, so that an intermittently connected verifier can check it offline. Each object binds its image hash, its name, its provenance record, and its source identity in one signature, and it carries its own key documents and authorization chain. Trust anchors are Decentralized Identifiers computed as key thumbprints, so no registry, ledger, or certificate authority is queried during verification. Our central technical point is that a signed hash alone gives only name-bound replay prevention. We therefore add temporal layers that such schemes usually omit: a freshness mechanism with interactive, beacon, and transparency log variants; signed status lists with a proven bounded staleness revocation guarantee; and monotone epochs that resist rollback of rotated keys and documents. We prove the base goals by reduction to signature unforgeability and hash collision resistance under a Dolev–Yao adversary, and we prove the temporal properties as unbounded inductive invariants discharged in Z3. An Ed25519 and SHA-256 implementation verifies a typical image in under two milliseconds with about 1.6 kB of metadata. The evidentiary levels are stated separately and are not interchangeable. The base object is proven, implemented, and measured; the freshness, revocation, and rollback layers are proven but not measured; the pseudonymous mode is design-only. “Self-verifiable” means that provenance is checked cryptographically from the object and one anchor. It does not mean the scheme proves that the captured scene is real, and it is conditional on a preconfigured root identifier and, for the temporal layers, on a status list or time source. Full article
(This article belongs to the Section Internet of Things)
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26 pages, 3160 KB  
Article
Complex Krawtchouk and Hahn Polynomial Operators for Localized and Numerically Stable Discrete Image Enhancement
by Hasan Bayram, Sibel Yalçın and Alina Alb Lupaş
Mathematics 2026, 14(15), 2711; https://doi.org/10.3390/math14152711 - 30 Jul 2026
Viewed by 322
Abstract
The Krawtchouk and Hahn families are discrete orthogonal polynomials defined on the integer pixel grid, yet as polynomials, they are entire functions of a complex variable. Adopting this complex variable and complex-valued viewpoint, we develop an image enhancement framework that connects discrete orthogonal [...] Read more.
The Krawtchouk and Hahn families are discrete orthogonal polynomials defined on the integer pixel grid, yet as polynomials, they are entire functions of a complex variable. Adopting this complex variable and complex-valued viewpoint, we develop an image enhancement framework that connects discrete orthogonal polynomial theory with geometric function theory. Two operators are introduced. The Krawtchouk operator exploits the binomial weight, for which the parameter p concentrates the basis around a selectable tonal level x=pN, producing a localized contrast enhancement steerable toward shadows, midtones, or highlights. The Hahn operator uses the two-parameter Hahn polynomials, the discrete analogue of the Jacobi family, in which (α,β) give asymmetric control of dark and light bands. Each operator is the real restriction of a holomorphic near identity map F(z)=z+kckϕ˜k(z), with the intensity entering the discrete basis through x=NI, realized as a monotone 256-entry lookup table. We prove a bounded deviation estimate |Fid|k|ck| on the intensity segment [0, 1] and a positive slope condition that, via the Noshiro–Warschawski criterion, is a univalence condition for the analytic transfer map, ruling out intensity order reversal and oscillatory folding. Because Hahn polynomials lose orthogonality at high order in naive arithmetic, we show that a three-term recurrence with log-gamma weights preserves orthonormality to within about 1010 on the full 8-bit grid, where single precision computation fails, and that the same scheme remains at the double-precision roundoff level on 10-, 12-, and 16-bit grids (N=1023,4095,65,535). The operators cost O(mL) table construction plus one lookup per pixel (about 3 ms for a 1024×1024 color image), and a histogram-based differential entropy criterion selects the focus parameters automatically. Experiments on imagery of fine art, wildlife, archaeology, and architecture show that the Krawtchouk operator yields stronger localized contrast compared to seven classical methods, while the Hahn operator attains higher PSNR/SSIM, both as deterministic fast slope-controlled transforms. A diffusion MRI example further demonstrates that matching the focus parameter to the tonal mass adapts the same operators to dark-dominated medical scan imagery. Full article
(This article belongs to the Section C: Mathematical Analysis)
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32 pages, 21854 KB  
Review
Advancements in MV2O6-Based Particulate Systems for Solar-Light Water Splitting
by Parnapalle Ravi and Jin-Seo Noh
Micromachines 2026, 17(8), 904; https://doi.org/10.3390/mi17080904 - 29 Jul 2026
Viewed by 268
Abstract
The development of efficient visible-light-driven semiconductor photocatalysts is essential for scalable and sustainable green hydrogen production. Among ternary metal oxides, MV2O6 (M = Zn, Ni, Cu, Mn, Co, etc.) metavanadates have attracted considerable interest because of their narrow band gaps [...] Read more.
The development of efficient visible-light-driven semiconductor photocatalysts is essential for scalable and sustainable green hydrogen production. Among ternary metal oxides, MV2O6 (M = Zn, Ni, Cu, Mn, Co, etc.) metavanadates have attracted considerable interest because of their narrow band gaps (~1.8–2.5 eV), strong visible-light absorption, and unique edge-sharing VO6 octahedral framework that promotes charge separation. This review summarizes recent advances in the design, synthesis, and electronic engineering of MV2O6-based photocatalysts for solar water splitting. Since direct particulate overall water splitting has only been demonstrated for MnV2O6, whereas ZnV2O6, NiV2O6, and CuV2O6 have mainly been investigated as photoelectrodes, both particulate photocatalytic and photoelectrochemical (PEC) systems are critically examined. The review clearly distinguishes these two configurations, highlighting how PEC studies provide valuable insights into charge transport, interfacial processes, and reaction kinetics while recognizing the additional challenges associated with suspension-based photocatalysis. Fundamental crystal structures, electronic band alignments, and charge-transfer characteristics of MV2O6 compounds are discussed, followed by recent advances in synthesis strategies, including hydrothermal, sol–gel, and deep eutectic solvent (DES)-assisted methods, together with morphology and defect engineering. Particular attention is given to oxygen-vacancy formation and its influence on visible-light absorption and charge separation. Modification strategies, including elemental doping, cocatalyst loading, and the construction of Z-scheme and step-scheme (S-scheme) heterojunctions, are critically evaluated for improving photocatalytic efficiency. Finally, the review discusses the key challenges that limit practical applications, including unfavorable band-edge positions, rapid carrier recombination, sluggish surface reaction kinetics, photostability, and the need to establish composition–structure–activity relationships. Future perspectives emphasize rational materials design through advanced characterization, theoretical calculations, and scalable synthesis approaches to accelerate the development of efficient MV2O6 photocatalysts for solar-driven hydrogen production. Full article
(This article belongs to the Special Issue Emerging Technologies and Applications for Semiconductor Industry)
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16 pages, 2626 KB  
Article
Amorphization-Enabled Direct Z-Scheme CdSe/MoSex Heterojunction for Enhanced Photocatalysis
by Lie Tian, Rong Wu, HaiYang Liu, Dong Zhang and Xiangqian Shen
Crystals 2026, 16(8), 495; https://doi.org/10.3390/cryst16080495 - 28 Jul 2026
Viewed by 299
Abstract
Organic pollutant degradation demands photocatalysts that couple efficient charge separation with strong redox capability. Direct Z-scheme heterojunction architectures fulfill these requirements and are consequently considered promising candidates. However, the rational design of such systems continues to present a major obstacle. Herein, a CdSe/amorphous [...] Read more.
Organic pollutant degradation demands photocatalysts that couple efficient charge separation with strong redox capability. Direct Z-scheme heterojunction architectures fulfill these requirements and are consequently considered promising candidates. However, the rational design of such systems continues to present a major obstacle. Herein, a CdSe/amorphous MoSex (CdSe/a-MoSex) direct Z-scheme heterojunction was successfully synthesized via a simple solid-state grinding and low-temperature hydrothermal method. Within 120 min under visible-light irradiation, methylene blue (MB, 40 mg/L) was degraded to 97.3% efficiency by the CdSe/a-MoSex heterojunction, whose photocatalytic activity markedly exceeded that of pristine CdSe and a-MoSex. Intimate interfacial contact between CdSe and a-MoSex enables photogenerated carriers to separate and migrate more efficiently, underpinning the observed performance enhancement. Moreover, the suitable band alignment derived from valence-band (VB) XPS and Mott-Schottky measurements supports the formation of a direct Z-scheme charge-transfer pathway. The Z-scheme mechanism effectively inhibits electron-hole recombination while maintaining the robust oxidation and reduction capabilities of the photogenerated carriers. This study offers a straightforward approach for fabricating CdSe/a-MoSex direct Z-scheme heterojunctions for the efficient photocatalytic degradation of organic pollutants. Full article
(This article belongs to the Section Materials for Energy Applications)
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86 pages, 18307 KB  
Review
CdS-Based Photocatalysts for Antimicrobial Applications: From Quantum Dots to Z-Scheme Heterojunctions—Mechanisms, Challenges, and Future Perspectives
by Nurlan Almas, Mirat Karibayev, Saparbek Tugelbay, Aliya Assilbekova, Irina Irgibaeva, Nursultan Mussakhanuly, Sergei Piskunov, Galiya Baisalova and Anuar Aldongarov
Molecules 2026, 31(15), 2626; https://doi.org/10.3390/molecules31152626 - 28 Jul 2026
Viewed by 448
Abstract
The chronic overuse of antibiotics has accelerated the emergence of antibiotic-resistant bacteria, creating a global public health crisis as conventional therapies fail against multidrug-resistant pathogens spreading through water and food chains. Cadmium sulfide (CdS) has been established as an important visible-light-driven photocatalyst for [...] Read more.
The chronic overuse of antibiotics has accelerated the emergence of antibiotic-resistant bacteria, creating a global public health crisis as conventional therapies fail against multidrug-resistant pathogens spreading through water and food chains. Cadmium sulfide (CdS) has been established as an important visible-light-driven photocatalyst for antibacterial applications. This brief review systematically examines the structure–property relationships governing CdS-based antibacterial materials, including crystallographic polymorphs (cubic sphalerite and hexagonal wurtzite), morphological diversity from quantum dots to hierarchical architectures, and synthesis methodologies that critically influence particle size, crystallinity, and surface chemistry. The mechanisms of antibacterial action are elucidated, encompassing photocatalytic reactive oxygen species (ROS) generation, controlled Cd2+ ion release, and membrane disruption. A detailed tabulated analysis is presented across three material classes: pristine CdS, binary composites, and ternary Z-scheme heterostructures. Density functional theory (DFT) calculations and molecular docking simulations provide atomic-level insights into charge transfer dynamics and enzyme inhibition mechanisms. Finally, critical challenges, photocorrosion, toxicity, biocompatibility concerns, and scalability limitations are addressed. This review bridges fundamental materials science with antimicrobial applications to guide rational design of next-generation CdS-based antibacterial materials. Full article
(This article belongs to the Section Photochemistry)
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16 pages, 5494 KB  
Article
Quality Control in Soil Analysis Through Interlaboratory Proficiency Tests
by Caterina Mazzoni, Thanh Thuy Nguyen, Nicolas Proix, Anne Tirard and Abdelkader Boubetra
Appl. Sci. 2026, 16(15), 7384; https://doi.org/10.3390/app16157384 - 23 Jul 2026
Viewed by 326
Abstract
Soil analysis is an important source of information in agriculture and environmental monitoring. However, analytical laboratories are subject to an increasing number of regulatory and accreditation requirements regarding the reliability of their test results. Participation in interlaboratory proficiency tests provides an essential tool [...] Read more.
Soil analysis is an important source of information in agriculture and environmental monitoring. However, analytical laboratories are subject to an increasing number of regulatory and accreditation requirements regarding the reliability of their test results. Participation in interlaboratory proficiency tests provides an essential tool to demonstrate the analytical performance of laboratories. This paper describes the results obtained from four proficiency tests evaluating 27 laboratories applying 12 standardized methods to measure key soil properties (moisture, pH, P2O5, exchangeable cations, organic carbon, and nitrogen) in two different batches of agricultural soil tested in blind replicates under time-different intermediate-precision conditions. This involved laboratories blindly analyzing two soil samples over a period of 17 and 28 months, respectively, with the aim of assessing the long-term consistency of laboratory performance. Various statistical and graphical methods, including Algorithm-A-based robust estimation of the assigned value, z-scores, z*-scores, and Youden plots, were used to assess individual laboratory performance. More than 80% of the participating laboratories showed satisfactory performance in all these tests. The results of this study highlight the robustness of the time-different blind testing in controlling the analytical performance of laboratories in soil analysis. Beyond conventional proficiency testing schemes, the present study provided laboratories with a unique framework to demonstrate their ability to sustain a high level of analytical performance, under intermediate-precision conditions, over an extended period. Full article
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